摘要
Let Ω(∈) Rn be a bounded convex domain with C2 boundary. For 0 ＜ p,q ≤∞ and a normal weight ψ, the mixed norm space Hp,q,ψk,(Ω) consists of all polyharmonic functions f of order k for which the mixed norm ||·||p,q,ψ＜∞.In this paper, we prove that the Gleason's problem (Ω,a,Hp,q,ψk) is always solvable for any reference point a ∈Ω. Also, the Gleason's problem for the polyharmonic ψ-Bloch (little ψ-Bloch) space is solvable. The parallel results for the hyperbolic harmonic mixed norm space are obtained.
LetΩ Rn be a bounded convex domain with C2 boundary. For 0<p,q≤∞and a normal weightψ. the mixed norm space Hp,q,ψk(Ω) consists of all polyharmonic functions f of order k for which the mixed norm‖·‖p,q,ψ<∞. In this paper, we prove that the Gleason's problem (Ω, a,Hp,q,ψk) is always solvable for any reference point a∈Ω. Also, the Gleason's problem for the polyharmonicψ-Bloch (littleψ-Bloch) space is solvable. The parallel results for the hyperbolic harmonic mixed norm space are obtained.
基金
This work is partially supported by the National Natural Science Foundation of China(Grant No.10471039)
the Natural Science Foundation of Zhejiang Province(Grant No.M103104).The authors thank the referee for his(her)valuable suggestion.
